{"defaultlang":"zh","titlegroup":{"articletitle":[{"lang":"zh","data":[{"name":"text","data":"切点约束和探针针尖半径补偿的金刚石刀具刃口钝圆半径求解方法"}]},{"lang":"en","data":[{"name":"text","data":"Calculating method for circle radius of diamond tool edge based on tangent point constrain and probe tip radius compensation"}]}]},"contribgroup":{"author":[{"name":[{"lang":"zh","surname":"雷","givenname":"大江","namestyle":"eastern","prefix":""},{"lang":"en","surname":"LEI","givenname":"Da-jiang","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":""}],"role":["corresp","first-author"],"corresp":[{"rid":"cor1","lang":"en","text":"LEI Da-jiang, E-mail:leidajiang@163.com","data":[{"name":"text","data":"LEI Da-jiang, E-mail:leidajiang@163.com"}]}],"bio":[{"lang":"zh","text":["雷大江(1974-), 男, 四川达州人, 高级工程师, 1996年于西安石油学院获得学士学位, 2002年于武汉科技大学获得硕士学位, 主要从事超精密加工及检测方面的研究。E-mail:leidajiang@163.com"],"graphic":[],"data":[[{"name":"bold","data":[{"name":"text","data":"雷大江"}]},{"name":"text","data":"(1974-), 男, 四川达州人, 高级工程师, 1996年于西安石油学院获得学士学位, 2002年于武汉科技大学获得硕士学位, 主要从事超精密加工及检测方面的研究。E-mail:"},{"name":"text","data":"leidajiang@163.com"}]]}],"email":"leidajiang@163.com","deceased":false},{"name":[{"lang":"zh","surname":"岳","givenname":"晓斌","namestyle":"eastern","prefix":""},{"lang":"en","surname":"YUE","givenname":"Xiao-bing","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":""}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"崔","givenname":"海龙","namestyle":"eastern","prefix":""},{"lang":"en","surname":"CUI","givenname":"Hai-long","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":""}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"张","givenname":"晓峰","namestyle":"eastern","prefix":""},{"lang":"en","surname":"ZHANG","givenname":"Xiao-feng","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":""}],"role":[],"deceased":false},{"name":[{"lang":"zh","surname":"张","givenname":"新疆","namestyle":"eastern","prefix":""},{"lang":"en","surname":"ZHANG","givenname":"Xin-jiang","namestyle":"western","prefix":""}],"stringName":[],"aff":[{"rid":"aff1","text":""}],"role":[],"deceased":false}],"aff":[{"id":"aff1","intro":[{"lang":"zh","label":"","text":"中国工程物理研究院 机械制造工艺研究所, 四川 绵阳 621900","data":[{"name":"text","data":"中国工程物理研究院 机械制造工艺研究所, 四川 绵阳 621900"}]},{"lang":"en","label":"","text":"Institute of Mechinery Manufacturing Technology, China Academy of Engineering Physics, Mianyang 621900, China","data":[{"name":"text","data":"Institute of Mechinery Manufacturing Technology, China Academy of Engineering Physics, Mianyang 621900, China"}]}]}]},"abstracts":[{"lang":"zh","data":[{"name":"p","data":[{"name":"text","data":"本文对金刚石刀具刃口钝圆半径求解方法展开研究，以有效提升金刚石刀具刃口锋利度的测量精度。文中分析了原子力显微镜（AFM）扫描探针几何形貌对金刚石刀具刃口锋利度测量结果的影响，并提出了基于切点约束和AFM探针针尖半径补偿的刀具刃口钝圆半径求解方法；讨论了消噪滤波、测量角度误差以及切点分离方法对测量结果的影响；在高精度测量平台上完成了金刚石刀具刃口锋利度测量，并将被测量的刀具用于飞切加工KDP晶体。结果表明：提出的刃口钝圆半径求解方法能够准确求解金刚石刀具的刃口锋利度，测量结果能很好地描述金刚石刀具的刃口锋利程度，可以为金刚石超精密切削加工的选刀和用刀提供有效指导。"}]}]},{"lang":"en","data":[{"name":"p","data":[{"name":"text","data":"To increase measuring precision of cutting edge sharpness of diamond tool effectively, a solution method of edge circle radius of diamond tool was researched. Influence of geometrical morphology of scanning probe of Atomic Force Microscope (AFM) on measuring result of cutting edge sharpness of diamond tool was analyzed, and solution method of circle radius of cutting edge based on tangency point constraint and probe tip radius compensation of AFM was proposed. Influence of noise filtering, measuring angle error and separation method of tangency point on measuring result was discussed. Measuring of cutting edge sharpness of diamond tool was completed on ultra-precision measuring platform, and measured tool was used for fly-cutting of KDP crystal. Result indicates that cutting edge sharpness of diamond tool can be accurately solved with proposed method, and measuring result can describe cutting edge sharpness of diamond tool well to provide effective guidance for cutter selection and using of ultra-precision cutting processing of diamond."}]}]}],"keyword":[{"lang":"zh","data":[[{"name":"text","data":"金刚石刀具"}],[{"name":"text","data":"刃口钝圆半径"}],[{"name":"text","data":"切点约束"}],[{"name":"text","data":"针尖半径补偿"}]]},{"lang":"en","data":[[{"name":"text","data":"diamond tool"}],[{"name":"text","data":"circle radius of cutting edge"}],[{"name":"text","data":"tangent constraint"}],[{"name":"text","data":"probe tip radius compensation"}]]}],"highlights":[],"body":[{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"1"}],"title":[{"name":"text","data":"引言"}],"level":"1","id":"s1"}},{"name":"p","data":[{"name":"text","data":"超精密切削加工是现代高科技产业和前沿科技发展的关键技术，而高精度金刚石刀具是实现超精密切削的基本条件之一"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"1","type":"bibr","rid":"b1","data":[{"name":"text","data":"1"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"3","type":"bibr","rid":"b3","data":[{"name":"text","data":"3"}]}}],"rid":["b1","b2","b3"],"text":"1-3","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"。对刀具刃口质量进行准确评价可为超精密切削过程中工件质量的监控、判定及选刀、用刀提供技术支撑。但由于表征金刚石刀具刃口质量的关键技术指标要求极高、测量困难，至目前为止，国际上尚未建立出一套相对统一、完善的金刚石刀具刃口质量关键技术指标评价模型。刀具刃口质量评价技术已成为制约金刚石刀具超精密切削技术进一步发展的重要因素之一。"}]},{"name":"p","data":[{"name":"text","data":"金刚石刀具锋利度是刃口质量的核心技术指标，其对被加工工件表面的粗糙度、表面缺陷、残余应力等均有重要影响"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"4","type":"bibr","rid":"b4","data":[{"name":"text","data":"4"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"8","type":"bibr","rid":"b8","data":[{"name":"text","data":"8"}]}}],"rid":["b4","b5","b6","b7","b8"],"text":"4-8","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"。近几十年来，国内外学者和相关研究机构针对刀具刃口锋利度的评价模型开展了大量的研究工作，取得了许多重要成果。具有代表性的如日本中山一雄、东芝机械浅井昭一、美国Oklahoma大学的Lucca、日本东北大学的高伟、新家坡国立大学Li、我国哈尔滨工业大学的袁哲俊、孙涛等人。他们采用扫描电镜(SEM)法、改进的SEM法和原子力显微镜(AFM)法直接或间接获得了测量数据，并以圆和抛物线作为理想拟合曲线对测量数据进行拟合，建立了刃口锋利度评价模型"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"9","type":"bibr","rid":"b9","data":[{"name":"text","data":"9"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"14","type":"bibr","rid":"b14","data":[{"name":"text","data":"14"}]}}],"rid":["b9","b10","b11","b12","b13","b14"],"text":"9-14","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"。但是，分析上述研究可以发现，所建立的圆拟合模型对拟合时的选点位置非常敏感，点的位置对评价结果有较大的影响；抛物线拟合虽然较圆拟合更为客观地描述了刃口锋利度的形状，但评价结果并不直观。同时，研究表明，相较于SEM法而言，AFM法具有更高的精度，能适应50 nm以下量级的刀具刃口锋利度的测量需求。在上述研究的基础上，德国汉诺威大学的Denkena等"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"15","type":"bibr","rid":"b15","data":[{"name":"text","data":"15"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"16","type":"bibr","rid":"b16","data":[{"name":"text","data":"16"}]}}],"rid":["b15","b16"],"text":"15-16","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"采用形状系数方法来评价刃口锋利度，他通过采用额外参数更精确地描述和评价刃口锋利度；由于形状系数方法这种多参数的评价模型在应用上有诸多局限，瑞士苏黎世制造研究所的Wyen等"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"17","type":"bibr","rid":"b17","data":[{"name":"text","data":"17"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"基于圆拟合评价模型开发了一种迭代算法，其通过多次迭代来选择圆拟合的数据点；Uhlmann等人"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"18","type":"bibr","rid":"b18","data":[{"name":"text","data":"18"}]}},{"name":"text","data":"]"}]},{"name":"text","data":"提出了一种使用特征曲线来评价刃口锋利度的方法，该特征曲线由实际刀面和间隙角组成，并假定切削刃轮廓的顶点是前刀面到后刀面转化的顶点。"}]},{"name":"p","data":[{"name":"text","data":"分析上述国内外学者关于刀具刃口锋利度评价模型的研究可以发现：刃口钝圆半径仍是评价金刚石刀具刃口锋利度的主要方法，但需要较好解决圆拟合方法中拟合点选取的难题。除此之外，采用AFM法时，探针针尖的几何尺寸与高精度金刚石刀具刃口锋利度的尺寸接近，有较明显的尺寸效应"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"blockXref","data":{"data":[{"name":"xref","data":{"text":"19","type":"bibr","rid":"b19","data":[{"name":"text","data":"19"}]}},{"name":"text","data":"-"},{"name":"xref","data":{"text":"20","type":"bibr","rid":"b20","data":[{"name":"text","data":"20"}]}}],"rid":["b19","b20"],"text":"19-20","type":"bibr"}},{"name":"text","data":"]"}]},{"name":"text","data":"，而现有圆拟合评价模型中在求解刀具刃口钝圆半径时并未考虑此因素。"}]},{"name":"p","data":[{"name":"text","data":"本文在前人研究的基础上，基于圆拟合评价模型，针对现有金刚石刀具刃口锋利度圆拟合评价模型中拟合点的选点难题，并考虑AFM扫描探针针尖的尺寸效应问题，构建了基于切点约束和原子力针尖半径补偿的刀具刃口钝圆半径求解方法；在测量平台上完成了刀具刃口锋利度的测量和评价并讨论了测量数据滤波消噪、刃口轮廓法向截面矫正、切点分离等问题；最后通过采用飞刀切削加工KDP晶体实验，验证了本文提出的金刚石刀具刃口钝圆半径求解方法的有效性。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2"}],"title":[{"name":"text","data":"切点约束和针尖半径补偿的刀具刃口钝圆半径求解方法"}],"level":"1","id":"s2"}},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"2.1"}],"title":[{"name":"text","data":"刃口钝圆方程及其基于AFM针尖半径补偿的修正"}],"level":"2","id":"s2-1"}},{"name":"p","data":[{"name":"text","data":"刀具刃口锋利度是由刀具前、后刀面基体材料不断去除逼近的结果决定的。本文采用金刚石刀具前、后刀面过渡区域的一小段圆弧的大小(即钝圆半径"},{"name":"italic","data":[{"name":"text","data":"r"},{"name":"sub","data":[{"name":"text","data":"ε"}]}]},{"name":"text","data":")来表征刀具刃口的锋利程度。这种表征方法较为直观，可用几何量严谨表达出一种可供测量的“锋利”特征，易于进行参数化描述和对比，如"},{"name":"xref","data":{"text":"图 1","type":"fig","rid":"Figure1","data":[{"name":"text","data":"图 1"}]}},{"name":"text","data":"所示。"}]},{"name":"fig","data":{"id":"Figure1","caption":[{"lang":"zh","label":[{"name":"text","data":"图1"}],"title":[{"name":"text","data":"金刚石刀具刃口锋利度"}]},{"lang":"en","label":[{"name":"text","data":"Fig 1"}],"title":[{"name":"text","data":"Edge sharpness of diamond tool"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703185&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703185&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703185&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"在刀具刃口钝圆半径的测量、求解过程中，通过AFM获取刀具刃口的数据点"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"x"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"=["},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"…"},{"name":"italic","data":[{"name":"text","data":"x"},{"name":"sub","data":[{"name":"text","data":"n"}]}]},{"name":"text","data":"]和"},{"name":"italic","data":[{"name":"text","data":"z"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"=["},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"…"},{"name":"italic","data":[{"name":"text","data":"z"},{"name":"sub","data":[{"name":"text","data":"n"}]}]},{"name":"text","data":"]，则刀具刃口钝圆方程可表示为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"1"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703204&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703204&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703204&type=middle"}}}],"id":"gxjmgc-25-7-1807-E1"}}]},{"name":"p","data":[{"name":"text","data":"由于AFM探针并不是理想的尖点，它的顶部是一段微小圆弧，当探针针尖的几何尺寸与被测物的轮廓特征近似时，实际测量的接触点是变化的，此时得到的数据与实际数据点将发生偏离。该现象即形貌膨胀，如"},{"name":"xref","data":{"text":"图 2","type":"fig","rid":"Figure2","data":[{"name":"text","data":"图 2"}]}},{"name":"text","data":"所示。由于常用AFM探针的尖锥半径大约为2~10 nm，而高品质金刚石刀具的刃口锋利度可低至20 nm以下，两者几乎相近，故需对AFM探针获得的测量数据进行修正。"}]},{"name":"fig","data":{"id":"Figure2","caption":[{"lang":"zh","label":[{"name":"text","data":"图2"}],"title":[{"name":"text","data":"形貌膨胀图"}]},{"lang":"en","label":[{"name":"text","data":"Fig 2"}],"title":[{"name":"text","data":"Measurement deviation"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703224&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703224&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703224&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"AFM针尖尺寸效应的测量模型如"},{"name":"xref","data":{"text":"图 3","type":"fig","rid":"Figure3","data":[{"name":"text","data":"图 3"}]}},{"name":"text","data":"所示，扫描探针的侧面与刀具刃口区域在"},{"name":"italic","data":[{"name":"text","data":"B"}]},{"name":"text","data":"点接触，"},{"name":"italic","data":[{"name":"text","data":"L"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"表示测量曲线，"},{"name":"italic","data":[{"name":"text","data":"L"}]},{"name":"text","data":"表示实际曲线，AFM探针针尖半径为"},{"name":"italic","data":[{"name":"text","data":"r"}]},{"name":"text","data":"′，探针针尖的圆心为"},{"name":"italic","data":[{"name":"text","data":"O"},{"name":"sub","data":[{"name":"text","data":"r"}]}]},{"name":"text","data":"′，过B有一条直线与圆弧"},{"name":"italic","data":[{"name":"text","data":"L"}]},{"name":"text","data":"相切，切线与"},{"name":"italic","data":[{"name":"text","data":"OA"}]},{"name":"text","data":"的交点为"},{"name":"italic","data":[{"name":"text","data":"A"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"，测量得到的是虚假形貌点"},{"name":"italic","data":[{"name":"text","data":"A"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"，而不是真实点"},{"name":"italic","data":[{"name":"text","data":"A"}]},{"name":"text","data":"。"}]},{"name":"fig","data":{"id":"Figure3","caption":[{"lang":"zh","label":[{"name":"text","data":"图3"}],"title":[{"name":"text","data":"测量模型"}]},{"lang":"en","label":[{"name":"text","data":"Fig 3"}],"title":[{"name":"text","data":"Measurement model"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703255&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703255&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703255&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"以"},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"text","data":"′"},{"name":"sub","data":[{"name":"italic","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"(即"},{"name":"italic","data":[{"name":"text","data":"x"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"A"}]},{"name":"text","data":")表示实际高度值，"},{"name":"italic","data":[{"name":"text","data":"z"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"(即"},{"name":"italic","data":[{"name":"text","data":"x"},{"name":"sub","data":[{"name":"text","data":"i"}]},{"name":"text","data":"A"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":")表示测量获得的高度值，根据"},{"name":"xref","data":{"text":"图 3","type":"fig","rid":"Figure3","data":[{"name":"text","data":"图 3"}]}},{"name":"text","data":"可得："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"2"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  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4","type":"fig","rid":"Figure4","data":[{"name":"text","data":"图 4"}]}},{"name":"text","data":"所示。相较于只考虑刃口钝圆区域而言，基于切点的约束方法更加贴合实际。"}]},{"name":"fig","data":{"id":"Figure4","caption":[{"lang":"zh","label":[{"name":"text","data":"图4"}],"title":[{"name":"text","data":"基于切点约束的刃口钝圆半径求解方法"}]},{"lang":"en","label":[{"name":"text","data":"Fig 4"}],"title":[{"name":"text","data":"Calculation method for circle radius of tool edge based on point of tangency constrain"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703406&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703406&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703406&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"基于最小二乘法，得到表达式："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"7"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703422&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703422&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703422&type=middle"}}}],"id":"gxjmgc-25-7-1807-E7"}}]},{"name":"p","data":[{"name":"text","data":"式中："},{"name":"italic","data":[{"name":"text","data":"x"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"为截面内数据点的分布距离；"},{"name":"italic","data":[{"name":"text","data":"z′"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"为截面内数据点的实际高度值；"},{"name":"italic","data":[{"name":"text","data":"η"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"为残差。"}]},{"name":"p","data":[{"name":"text","data":"前刀面约束直线(截面线)可表示为"},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"text","data":"′="},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"+"},{"name":"italic","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"，而后刀面约束直线(截面线)可表示为"},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"text","data":"′="},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"+"},{"name":"italic","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"，其中"},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"、"},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"、"},{"name":"italic","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"、"},{"name":"italic","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"可采用最小二乘法拟合实验数据得到。"}]},{"name":"p","data":[{"name":"text","data":"前、后刀面截面线的夹角平分线可以表示为"},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"text","data":"′="},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"+"},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"－1)－"},{"name":"italic","data":[{"name":"text","data":"c"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"。其中："},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"sub","data":[{"name":"text","data":"3"}]},{"name":"text","data":"=1+"},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":"("},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"－"},{"name":"italic","data":[{"name":"text","data":"k"}]},{"name":"sub","data":[{"name":"text","data":"2"}]},{"name":"text","data":")；"}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703444&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703444&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703444&type=middle"}}}],"id":"gxjmgc-25-7-1807-FE2"}}]},{"name":"p","data":[{"name":"text","data":"则相切约束条件为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703466&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703466&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703466&type=middle"}}}],"id":"gxjmgc-25-7-1807-FE3"}}]},{"name":"p","data":[{"name":"text","data":"若使总误差最小，则有："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"8"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703489&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703489&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703489&type=middle"}}}],"id":"gxjmgc-25-7-1807-E8"}}]},{"name":"p","data":[{"name":"text","data":"即可得到刃口钝圆半径"},{"name":"italic","data":[{"name":"text","data":"r"},{"name":"sub","data":[{"name":"text","data":"ε"}]}]},{"name":"text","data":"的表达式为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[{"name":"text","data":"9"}],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703515&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703515&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703515&type=middle"}}}],"id":"gxjmgc-25-7-1807-E9"}}]},{"name":"p","data":[{"name":"text","data":"式中"},{"name":"italic","data":[{"name":"text","data":"T"}]},{"name":"text","data":"是与前后刀面倾斜角度相关的半径约束因子，可表示为："}]},{"name":"p","data":[{"name":"dispformula","data":{"label":[],"data":[{"name":"text","data":" "},{"name":"text","data":"  "},{"name":"math","data":{"graphicsData":{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703539&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703539&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703539&type=middle"}}}],"id":"gxjmgc-25-7-1807-FE4"}}]}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3"}],"title":[{"name":"text","data":"讨论"}],"level":"1","id":"s3"}},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.1"}],"title":[{"name":"text","data":"数据消噪及滤波"}],"level":"2","id":"s3-1"}},{"name":"p","data":[{"name":"text","data":"虽然AFM扫描头具有pm级分辨率，但在实际测量过程中，由于受环境干扰和测量辅助装置的影响，会引入结构振动和噪声等掺杂信号，让最终采集到的刀具刃口轮廓数据失真。因此，在对测量数据进行计算和评估前，必须分析干扰信号的来源和性质，并对测量数据进行消噪滤波，以保证最终测量结果可靠。"}]},{"name":"p","data":[{"name":"xref","data":{"text":"图 5(a)","type":"fig","rid":"Figure5","data":[{"name":"text","data":"图 5(a)"}]}},{"name":"text","data":"是采用AFM扫描得到的刀具刃口轮廓截面图；从"},{"name":"xref","data":{"text":"图 5(b)","type":"fig","rid":"Figure5","data":[{"name":"text","data":"图 5(b)"}]}},{"name":"text","data":"可明显观察到截面轮廓中有干扰信号的存在，出现了很多“毛刺”，若不对其进行消噪滤波，必将对后续的数据处理和计算结果产生较大影响。对"},{"name":"xref","data":{"text":"图 5(b)","type":"fig","rid":"Figure5","data":[{"name":"text","data":"图 5(b)"}]}},{"name":"text","data":"进行中值滤波，如"},{"name":"xref","data":{"text":"图 5(c)","type":"fig","rid":"Figure5","data":[{"name":"text","data":"图 5(c)"}]}},{"name":"text","data":"所示，对比发现，滤波处理后的轮廓数据高频段的干扰几乎消失，而低频区域的功率谱幅值变化很小。这表明经过滤波之后噪声大幅减少，且轮廓信息损失极小。"}]},{"name":"fig","data":{"id":"Figure5","caption":[{"lang":"zh","label":[{"name":"text","data":"图5"}],"title":[{"name":"text","data":"受干扰的刀尖截面轮廓"}]},{"lang":"en","label":[{"name":"text","data":"Fig 5"}],"title":[{"name":"text","data":"Section of disturbed tool nose"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703555&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703555&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703555&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"常用的消噪滤波方法有很多，如中值滤波方法等"},{"name":"sup","data":[{"name":"text","data":"["},{"name":"xref","data":{"text":"21","type":"bibr","rid":"b21","data":[{"name":"text","data":"21"}]}},{"name":"text","data":"-22]"}]},{"name":"text","data":"，可根据测量数据分析干扰信号来源和性质，并采用合适的滤波方法对数据进行滤波消噪，以保证滤波后无明显噪声点、突变点，同时应注意保护图像细节，为后续的数据处理奠定基础。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.2"}],"title":[{"name":"text","data":"刃口轮廓数据的法向截面矫正"}],"level":"2","id":"s3-2"}},{"name":"p","data":[{"name":"text","data":"在测量过程中，由于刀具摆放姿态或扫描区域设置等原因，表面测量轮廓与理想轮廓之间会有一定的角度误差，所采集的刀具刃口区域的三维形貌数据如"},{"name":"xref","data":{"text":"图 6","type":"fig","rid":"Figure6","data":[{"name":"text","data":"图 6"}]}},{"name":"text","data":"所示。采用不同的截面线对刃口锋利度进行评价(如"},{"name":"xref","data":{"text":"图 6","type":"fig","rid":"Figure6","data":[{"name":"text","data":"图 6"}]}},{"name":"text","data":"中的截面线1和2)，若在计算时忽略角度误差的影响，则将导致最终刃口钝圆半径的计算值有较大的偏差。"}]},{"name":"fig","data":{"id":"Figure6","caption":[{"lang":"zh","label":[{"name":"text","data":"图6"}],"title":[{"name":"text","data":"刀具刃口"}]},{"lang":"en","label":[{"name":"text","data":"Fig 6"}],"title":[{"name":"text","data":"Cutting edge of tool nose"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703580&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703580&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703580&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"对于上述问题，可采用仿射变换等方法旋转刃口轮廓三维形貌数据，以获得刀具刃口法向轮廓数据。通过对刃口轮廓数据进行法向截面矫正，可以避免刃口钝圆半径求解时所产生的误差，这也与刀具的具体使用状况相符。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"3.3"}],"title":[{"name":"text","data":"切点分离"}],"level":"2","id":"s3-3"}},{"name":"p","data":[{"name":"text","data":"切点的选择在本文所述刀具刃口钝圆半径求解中至关重要，不同的选点将导致结果差异较大。本文所述求解方法中切点分离是在前、后刀面截面线约束条件下进行的。这也与刀具刃口的形成过程相吻合。通过所采集的与刀具刃口区域相关的前、后刀面数据点，获取刀具前、后刀面截面线，在切点约束条件下即可得到准确的切点，再在此条件下计算刃口钝圆半径。"}]}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"4"}],"title":[{"name":"text","data":"测量及切削实验"}],"level":"1","id":"s4"}},{"name":"p","data":[{"name":"text","data":"应用上述切点约束和探针针尖半径补偿的刀具刃口钝圆半径求解方法，在刀具测量装置(如"},{"name":"xref","data":{"text":"图 7","type":"fig","rid":"Figure7","data":[{"name":"text","data":"图 7"}]}},{"name":"text","data":"所示)上对刀具刃口锋利度进行测试和评价。"}]},{"name":"fig","data":{"id":"Figure7","caption":[{"lang":"zh","label":[{"name":"text","data":"图7"}],"title":[{"name":"text","data":"测量装置"}]},{"lang":"en","label":[{"name":"text","data":"Fig 7"}],"title":[{"name":"text","data":"Measurement equipment"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703602&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703602&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703602&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"主要步骤如下："}]},{"name":"p","data":[{"name":"text","data":"(1) 基本设置：包括刀具对准、AFM扫描范围、扫描速度和反馈增益等内容；"}]},{"name":"p","data":[{"name":"text","data":"(2) 原始数据获得与读取：获得刀具刃口的数据点"},{"name":"italic","data":[{"name":"bold","data":[{"name":"text","data":"x"}]},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"=["},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"…"},{"name":"italic","data":[{"name":"text","data":"x"},{"name":"sub","data":[{"name":"text","data":"n"}]}]},{"name":"text","data":"]和"},{"name":"italic","data":[{"name":"text","data":"z"},{"name":"sub","data":[{"name":"text","data":"i"}]}]},{"name":"text","data":"=["},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"sub","data":[{"name":"text","data":"1"}]},{"name":"text","data":"…"},{"name":"italic","data":[{"name":"text","data":"z"},{"name":"sub","data":[{"name":"text","data":"n"}]}]},{"name":"text","data":"]。"}]},{"name":"p","data":[{"name":"text","data":"(3) 数据消噪及滤波。"}]},{"name":"p","data":[{"name":"text","data":"(4) 法向截面轮廓提取，以保证所求得的刃口钝圆半径值在法向截面内。"}]},{"name":"p","data":[{"name":"text","data":"(5) 约束截面线、切点和刃口钝圆半径拟合点提取。"}]},{"name":"p","data":[{"name":"text","data":"(6) 刃口钝圆半径求解：基于文中的求解方法获得刀具刃口钝圆半径。"}]},{"name":"p","data":[{"name":"text","data":"基于MATLAB，开发测量数据处理及刃口钝圆半径求解程序，得到刀具刃口钝圆半径值，如"},{"name":"xref","data":{"text":"图 8","type":"fig","rid":"Figure8","data":[{"name":"text","data":"图 8"}]}},{"name":"text","data":"所示。根据实验测量数据，拟合得到的前、后刀面约束直线方程分别为"},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"text","data":"′=0.971"},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"+49.286、"},{"name":"italic","data":[{"name":"text","data":"z"}]},{"name":"text","data":"′=－0.989"},{"name":"italic","data":[{"name":"text","data":"x"}]},{"name":"text","data":"+53.571，相关系数分别为0.999 3和0.998，且在显著性水平为"},{"name":"italic","data":[{"name":"text","data":"α"}]},{"name":"text","data":"=0.05的条件下，得到的概率值"},{"name":"italic","data":[{"name":"text","data":"P"}]},{"name":"text","data":"小于0.001。"}]},{"name":"fig","data":{"id":"Figure8","caption":[{"lang":"zh","label":[{"name":"text","data":"图8"}],"title":[{"name":"text","data":"刃口钝圆半径测量结果"}]},{"lang":"en","label":[{"name":"text","data":"Fig 8"}],"title":[{"name":"text","data":"Measurement results of circle radius of cutting edge"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703621&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703621&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703621&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"针对两把金刚石刀具，以刀尖圆弧顶点为中心，在约±0.2 mm的范围内均匀地进行5点测量，测量结果如"},{"name":"xref","data":{"text":"表 1","type":"table","rid":"Table1","data":[{"name":"text","data":"表 1"}]}},{"name":"text","data":"所示。可以看出，编号1的刀具刃口钝圆半径均值"},{"name":"italic","data":[{"name":"text","data":"r"},{"name":"sub","data":[{"name":"text","data":"ε"}]}]},{"name":"text","data":"=77.2 nm，标准偏差"},{"name":"italic","data":[{"name":"text","data":"s"}]},{"name":"text","data":"=10.3nm，表明这把刀具所测区域的刃口锋利度一致性不够好，具有较大的离散性；而编号2的刀具刃口钝圆半径均值"},{"name":"italic","data":[{"name":"text","data":"r"},{"name":"sub","data":[{"name":"text","data":"ε"}]}]},{"name":"text","data":"=49.6 nm，标准偏差"},{"name":"italic","data":[{"name":"text","data":"s"}]},{"name":"text","data":"=3 nm，表明该把刀具所测区域的刃口锋利度一致性较好。"}]},{"name":"table","data":{"id":"Table1","caption":[{"lang":"zh","label":[{"name":"text","data":"表1"}],"title":[{"name":"text","data":"刀具刃口钝圆半径数据表"}]},{"lang":"en","label":[{"name":"text","data":"Table 1"}],"title":[{"name":"text","data":"Data of circle radius of cutting edge"}]}],"note":[],"table":[{"head":[[{"align":"center","style":"class:table_top_border","data":[{"name":"text","data":"刀具编号"}]},{"align":"center","style":"class:table_top_border","data":[{"name":"text","data":"点1"}]},{"align":"center","style":"class:table_top_border","data":[{"name":"text","data":"点2"}]},{"align":"center","style":"class:table_top_border","data":[{"name":"text","data":"点3"}]},{"align":"center","style":"class:table_top_border","data":[{"name":"text","data":"点4"}]},{"align":"center","style":"class:table_top_border","data":[{"name":"text","data":"点5"}]}]],"body":[[{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"1"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"84"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"76"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"71"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"80"}]},{"align":"center","style":"class:table_top_border2","data":[{"name":"text","data":"75"}]}],[{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"2"}]},{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"52"}]},{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"49"}]},{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"50"}]},{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"48"}]},{"align":"center","style":"class:table_bottom_border","data":[{"name":"text","data":"49"}]}]],"foot":[]}]}},{"name":"p","data":[{"name":"text","data":"分别将编号为1和2的两把刀具在同一台飞切机床上采用同样的切削工艺参数进行KDP晶体切削实验，如"},{"name":"xref","data":{"text":"图 9","type":"fig","rid":"Figure9","data":[{"name":"text","data":"图 9"}]}},{"name":"text","data":"，"},{"name":"xref","data":{"text":"10","type":"fig","rid":"Figure10","data":[{"name":"text","data":"10"}]}},{"name":"text","data":"所示。由图可知，得到的晶体表面形貌有较大不同：采用刀具1获得的晶体表面粗糙度在10 nm左右，沿着刀具切削方向有很多细碎的纹路；而采用刀具2获得的晶体表面粗糙度可在5 nm左右，晶体表面纹理较浅，形貌质量较好。"}]},{"name":"fig","data":{"id":"Figure9","caption":[{"lang":"zh","label":[{"name":"text","data":"图9"}],"title":[{"name":"text","data":"刀具1所获得的晶体表面形貌"}]},{"lang":"en","label":[{"name":"text","data":"Fig 9"}],"title":[{"name":"text","data":"Surface morphology of crystal by tool 1"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703640&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703640&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703640&type=middle"}]}},{"name":"fig","data":{"id":"Figure10","caption":[{"lang":"zh","label":[{"name":"text","data":"图10"}],"title":[{"name":"text","data":"刀具2所获得的晶体表面形貌"}]},{"lang":"en","label":[{"name":"text","data":"Fig 10"}],"title":[{"name":"text","data":"Surface morphology of crystal by tool 2"}]}],"subcaption":[],"note":[],"graphics":[{"print":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703657&type=","small":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703657&type=small","big":"http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=1703657&type=middle"}]}},{"name":"p","data":[{"name":"text","data":"从测量和切削实验结果可以看出，本文所构建的刃口钝圆半径求解方法较为准确地分离了不同刃口锋利度下的工件表面粗糙度和表面纹理结构。"}]}]},{"name":"sec","data":[{"name":"sectitle","data":{"label":[{"name":"text","data":"5"}],"title":[{"name":"text","data":"结论"}],"level":"1","id":"s5"}},{"name":"p","data":[{"name":"text","data":"本文分析了刀具刃口区域选点和AFM探针几何形貌对刃口钝圆半径求解结果的影响，建立了基于切点约束和AFM探针针尖半径补偿的刃口钝圆半径求解方法；在测量平台上完成了金刚石刀具刃口锋利度的测量和评价，并将所测刀具用于金刚石刀具飞切加工KDP晶体，切削实验结果表明：所建立的刃口钝圆半径求解方法能够较好地描述金刚石刀具刃口的锋利程度，验证了本文求解方法的有效性和测量结果的准确性。"}]}]}],"footnote":[],"reflist":{"title":[{"name":"text","data":"参考文献"}],"data":[{"id":"b1","label":"1","citation":[{"lang":"zh","text":[{"name":"text","data":"袁巨龙, 王志伟, 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